Inclined PLane Force problem

In summary, the problem involves an engine pulling two cars out of a mine on a sloping track with an angle of 22 degrees. Each car has a mass of 1.1x10^4 Kg and the engine can exert a maximum force of 1.6x10^5 N on car A. The question asks for the time it takes for the train to stop moving up the track if the force exerted by the engine on car A decreases at a constant rate of 2.9 N per second. Using the equations F= Fmax-2.9t and acceleration=(Fmax-2.9t-mgsin(x))/m, we can solve for T, which represents the time. The train
  • #1
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Homework Statement


Question:
An engine is used to pull a train of two cars out of a mine. The floor slopes upward at an angle of 22 degrees. Each car has a mass of 1.1x10^4 Kg and normally travels without friction on the tracks. The engine can exert a maximum force of 1.6x10^5 N on car A. If the engineer again throttles back so that the force exerted by the engine on car A decreases at the constant rate of 2.9 N per second, how long before the train stops moving up the track? Assume the original speed was 3.4 m/s

Homework Equations


F= Fmax-2.9t
acceleration=(Fmax-2.9t-mgsin(x))/m

The Attempt at a Solution


[(Fmax-mgsin(x))/m]T-[(1.45/m)]T^2=0
incase u havnt realized we're solving for "T"
 
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  • #2
[(1.6x10^5-1.1x10^4 x 9.8 xsin22)/1.1x10^4]T-[(1.45/1.1x10^4)]T^2=0[1.48x10^5/1.1x10^4]T-[1.45/1.1x10^4]T^2=01.34T-1.45T^2=0T^2-1.34T+1.45=0(T-1.09)(T-1.32)=0T=1.09 or T=1.32The train will stop moving up the track in 1.09 seconds or 1.32 seconds.
 
  • #3


I would approach this problem by first breaking down the given information and identifying the key variables and equations involved. From the statement, we can see that the problem involves a force (F), mass (m), acceleration (a), and time (t). Additionally, we are given the maximum force the engine can exert (Fmax) and the angle of inclination (x). Using the given equations, I would first find the acceleration of the train by plugging in the values for Fmax, m, and x. This will give me the acceleration in terms of t, which I can then use to solve for t by setting the equation equal to zero. This will give me the time it takes for the train to stop moving up the track.

Next, I would consider the implications of the engine throttling back at a constant rate of 2.9 N per second. This means that the force exerted by the engine on car A will decrease over time, leading to a decrease in acceleration. Therefore, I would need to modify the original equation to take into account this decrease in force. I would then use this new equation to solve for t once again.

Finally, I would compare the two values for t and determine the difference between them. This would give me the amount of time it takes for the train to stop moving up the track after the engine throttles back.

In conclusion, as a scientist, I would analyze the given information, use relevant equations to solve for the unknown variable, and consider any changes or modifications that may affect the final solution.
 

1. What is an inclined plane force problem?

An inclined plane force problem is a type of physics problem that involves calculating the forces acting on an object that is on an inclined plane. This can include the weight of the object, the normal force, and any other forces such as friction.

2. How do you calculate the forces on an object on an inclined plane?

To calculate the forces on an object on an inclined plane, you will need to use the basic force equations from Newton's laws of motion. This includes calculating the weight of the object, determining the angle of the incline, and taking into account any other forces such as friction.

3. What is the significance of an inclined plane in physics?

An inclined plane is important in physics because it allows us to simplify complex force problems, making them easier to solve. It also helps us understand the relationship between forces, motion, and energy.

4. How does the angle of an incline affect the forces on an object?

The angle of an incline can greatly affect the forces on an object. As the angle increases, the component of the weight acting in the direction of the incline will also increase, making it more difficult to move the object up the incline. Additionally, a steeper incline will result in a greater normal force acting on the object.

5. What are some real-life examples of inclined plane force problems?

Some common examples of inclined plane force problems include pushing a heavy object up a ramp, using a wheelchair ramp, and sliding down a playground slide. These scenarios all involve calculating the forces acting on an object on an inclined plane.

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